Experimental determination of the band structure of photonic crystals of colloidal silica spheres

A photonic band structure of colloidal crystals of silica spheres is analytically determined by a band model with three fitting parameters: the sphere size, the effective refractive index, and the band-gap. Optical properties of the crystals annealed at various temperatures were characterized by a procedure similar to X-ray diffraction technique, and the width of photonic band-gap measured from the transmission spectra experimentally servers as an additional check on the validation of the model. The photonic band structures defined by the band-gap, the refractive index, and the Brillouin zone are obviously superior to the use of the Bragg's expression involving simple zone folding.